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10 March, 22:10

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 - $ 343,000 - $ 50,000 1 52,000 24,700 2 72,000 22,700 3 72,000 20,200 4 447,000 15,300 Whichever project you choose, if any, you require a return of 16 percent on your investment. a-1 What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e. g., 32.16.)

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  1. 10 March, 22:21
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    The payback period for each of the project is - project A = 3.33 and project B = 2.13

    Explanation:

    First of all the payback period means the amount of time it would take for a company to recover its initial cost or investment which it has invested in the project.

    Calculating the payback period for project A

    Year Cash flow Cumulative Discounting Present Discounted

    cash flow factor value cumulative flow

    (NOTE - Formula used for discounting factor = 1 / (1 + i) ^n, where i = 16% which is the rate of return on the investment and n is the number of years.)

    0 - $343,000 - $343,000 1 - $343,000 - $343,000

    1 $52,000 - $291,000.86206 $44,828 - $298,172

    2 $72,000 - $219,000.74314 $53,508 - $244,665

    3 $72,000 - $147,000.64063 $46,127 - $198,537

    4 $447,000 $300,000.55226 $2,46,874 $48,337

    Now we will in which year the cash flow was last negative and then in that we will add (cumulative cash flow of the year it was last negative / cash flow of the next period).

    = 3 + $147,000 / $447,000

    = 3.33 (payback period for project A)

    Calculating the payback period for project B

    Year Cash flow Cumulative Discounting Present Discounted

    cash flow factor value cash flow

    0 - $50,000 - $50,000 1 - $50,000 - $50,000

    1 $24,700 - $25,300.86206 $21,293 - $28,707

    2 $22,700 - $2600.74314 $16,869 - $11,838

    3 $20,200 $17,600. 64063 $12,941 $1013

    4 $15,300 $32,900.55226 $8,450 $9463

    Now we will in which year the cash flow was last negative and then in that we will add (cumulative cash flow of the year it was last negative / cash flow of the next period).

    = 2 + 2600 / 20,200

    = 2.13 (payback period for project B)
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